INGEBRETSON-DISSERTATION-2018.pdf (2.63 MB)
Hausdorff Dimension of Kuperberg Minimal Sets
thesisposted on 2018-11-27, 00:00 authored by Daniel Ingebretson
In 1994, Kuperberg constructed a smooth flow on a three-manifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minimal set. We develop new techniques to study the symbolic dynamics and dimension theory of this minimal set, by relating it to the limit set of a graph directed pseudo-Markov system over a countable alphabet.
DepartmentMathematics, Statistics, and Computer Science
Degree GrantorUniversity of Illinois at Chicago